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### Revision(s):

Revision #1 to TR08-098 | 11th April 2009 00:00

#### A Hypergraph Dictatorship Test with Perfect Completeness

Revision #1
Authors: Victor Chen
Accepted on: 11th April 2009 00:00
Keywords:

Abstract:

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based $\PCP$ construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.

### Paper:

TR08-098 | 12th November 2008 00:00

#### A Hypergraph Dictatorship Test with Perfect Completeness

TR08-098
Authors: Victor Chen
Publication: 14th November 2008 16:34
Keywords:

Abstract:

A hypergraph dictatorship test is first introduced by Samorodnitsky
and Trevisan and serves as a key component in
their unique games based $\PCP$ construction. Such a test has oracle
are $o(1).$ Their test makes $q\geq3$ queries
and has amortized query complexity $1+O\left(\frac{\log q}{q}\right)$
completeness and amortized query complexity $1+O\left(\frac{\log q}{q}\right)$.